Studia Humana Volume 1:3/4 (2012), pp.59—65 Intensio: Leibniz in Creating a New Term for the Modal Logic Basil Lourié St. Petersburg Russia [email protected] Abstract: It is still difficult to say what the main source of Leibniz’s modal thinking was; at least, his acquaintance with the ideas of Spanish Jesuits about the “moral necessity” is to be dated to the epoch when the modal ideas already took shape in his mind. There was, however, one name normally referred to by Leibniz himself as his main predecessor in modal thinking, Richard Swineshead. In fact, Leibniz created his personal myth about Swineshead even before having read his works, and so, he attributed to Swineshead some of his own ideas, including the modal reinterpretation of the term intensio borrowed from the mediaeval physics. Leibniz’s achievements and intuitions in the field of intensional logics were evaluated, for the first time, by no other than the creator of the modern modal logic Clarence I. Lewis, whose seminal 1918 monograph contains a very important historical essay on Leibniz with addition of two translations of his pertinent works (published for the first time in 1903, but not acknowledged as important even then). [1, pp. 5-18, 373-387] Then, Leibniz’s ideas about intensionality were studied in a more systematic way by Nicholas Rescher, [2] another key figure in the twentieth-century modal logic. It is still a disputable matter, whether Leibniz had direct predecessors in his modal thinking. It is often thought that, in the matters of theodicy, he had ones – Spanish Jesuit thinkers of the seventeenth century who were teaching about the “moral necessity” for God and even the “possible worlds.” [3] It is certain that Leibniz did have access to their publications, although was not referring to them explicitly. However, Bartholomew Des Bosses, another Jesuit and a correspondent of Leibniz, who was the first to notice the parallels between these Jesuits’ and Leibniz’s thought, did not attribute to them any direct influence on Leibniz. [4, pp. 228/229 (lat./Eng. tr.) and 438, n. 5.]1 The German mystical thought of Weigel, F. M. van Helmont, and Böhme could also be a source of inspiration for Leibniz’s modal thinking, but this possibility remains unexplored, and, anyway, Leibniz did not recall any of them in explicitly modal contexts.2 Normally, Leibniz presented his ideas concerning the modal logic as his original ones. There is, however, a unique name which is often referred to in Leibniz’s works as his predecessor in modal thinking, Richard Swineshead. Moreover, Leibniz’s modal term intensio, so popular in the modern logic, goes back to Leibniz’s understanding of Swineshead. Probably, however, the modern historians of the modal logic had reason to pay little attention, if any, to Swineshead. Leibniz’s admiration toward Swineshead is a phenomenon whose value is somewhat independent from the historical personality of Swineshead as a scholar. *** Mary Spencer in her 1971 notice showed how the modern use of the term “intension” and its derivates goes back to Leibniz. [5] Since then, some previously unpublished Leibniz’s papers 59 became available, 3 and their contents allow us to grasp Leibniz’s intuition in a more adequate way. The scholastic background of Leibniz’s usage of intensio has been noticed but never traced, and this is the main reason to readdress the issue after Mary Spencer. In his earlier period, Leibniz knew the word intensio only in the sense of the late Scholasticism, where it was a physical term (roughly with the same meaning as the modern “intensity”)4 forming a pair with its antonym remissio. The fourteenth-century scholastic debate concerning “intensions” and “remissions” of forms was about physics. Leibniz, however, was thinking about physics in terms of semantics. Moreover, his way of thinking was influenced by the logic of Port Royal (1662) with its distinction between “extension” and “comprehension”5; it is rather obviously that the term “extension” in Leibniz’s usage goes back to Arnauld and Nicole. Somewhere before 1681, Leibniz started to develop a very high idea, if not a myth, about his alleged predecessor in Scholastics, Richard Swineshead (fl. ca. 1340–1355) nicknamed Calculator,6 then known to Leibniz only indirectly from the references by other authors (only one of them is called by name: Scaliger7). In one instance, Leibniz said that, judging from the works of Swineshead’s followers (“ejus sectatorum scripta”), their merits in applying mathematics “in media metaphysicorum” (“in the field of metaphysics”) must be praised, and, probably, they would anticipate “our works,” were they reached by “the presently achieved light of mathematics” (“lumen Mathematicorum quod nunc accensum est”). [6, p. 720] Leibniz’s attitude toward both Swineshead and Scholasticism is clear from the following passage: “Parmy les Scholastiques il y eut un certain Jean Suisset appellé le Calculateur, dont je n’ay encor pû trouver les ouvrages, n’ayant vue que ceux de quelques sectateurs qu’il avoit. Ce Suisset a commencé de faire le Mathematicien dans le Scholastique, mais peu de gens l’ont imité, parce qu’il auroit fallu quitter la methode [des] disputes pour celle des comptes et raisonnemens, et un trait de plume auroit epargné beaucoup de clameurs.”8 According to Leibniz’s impression which was already formed as early as in 1682, Swineshead must be placed alongside with Aristotle!9 In other instances, Leibniz enumerates Swineshead’s studies among the most important achievements in philosophy.10 It is obvious that Leibniz, long before reading Swineshead, already considered him as the inventor of logical “calculus,” the main goal of Leibniz’s own studies. When, in December 1689, Leibniz eventually found Swineshead’s incunabula in Florence, he was very glad and, of course, did not change his opinion.11 It was certainly a forcible interpretation of Swineshead’s legacy, but in our present situation of lacking detailed studies in Swineshead and even critical edition of his works12 it would be hasty to judge in what extent Leibniz was indulging in wishful thinking. The real Swineshead participated in the circle of British schoolmen which considered the qualities (“forms”) as able to change in intensity without being changed themselves (that is, remaining the same individual forms but differing in intensity).13 His main innovation in the field consisted in introducing a specific way of counting the quantity of a given form. He proposed to start from the zero grade (not from the maximum grade), and so, de facto to count only the “intension” (intensity), because the “remission” becomes an equivalent magnitude whose counting from the zero grade is inconvenient.14 This is basically the modern approach to measurement of physical magnitudes. Apparently, however, there is no sign that Swineshead himself applied his theory outside physics and considered it as a universal logical computus15—as his admirer Leibniz certainly did. In one of the earliest notices mentioning intensio, Leibniz gives the following definitions: “Intension is the quantity of the form itself, such as if the form is motion, intension would be speed. Extension of a form is the quantity of matter which is within the form of the same measure, such as the quantity of the moving body is the extension of the motion.”16 These definitions are still in Swineshead’s vein. But even before reading Swineshead Leibniz started to use the notion intension for the logic of natural language, for the phenomenon which we now call indexicality. Thus, he wrote: “In the pronouns, we have some intension, such as ego, egomet; tu, tute; ille, illemet or ille ipse, ipsemet.” [7, p. 888]17 This is not an intensional in the modern sense (such as in the Montague semantics), but simply a dimension of meaning. The indexicals, such as the pronouns, do not have a 60 function which ascribes to them denotations in each of the possible worlds (as does the intensional in Montague’s sense). Such was the background of the now famous Leibniz’s passage in the Nouveaux Essais sur l’entendement humain, IV, xvii, 8: “La maniere d’enoncer vulgaire regarde plustost les individus, mais celle d’Aristote a plus d’egard aux idées ou universaux.18 Car disant ‘tout homme est animal’, je veux dire que tous les hommes sont compris dans tous les animaux; mais j’entends en même temps que l’idée de l’animal est comprise dans l’idée de l’homme. L’animal comprend plus d’individus que l’homme, mais l’homme comprend plus d’idées ou plus de formalités; l’un a plus d’exemples, l’autre plus de degrés de realité; l’un a plus d’extension, l’autre plus d’intension.”[9, p. 486]19 Now Leibniz’s approach—which Leibniz himself considered as being Swineshead’s one— became called-for in the Quantum logics, where the physical phenomena are treated with the logical methods developed for the philosophy of language. Leibniz applied to the language the logical ideas inspired by Swineshead’s physics, but now the logicians of physics use logical ideas of the philosophy of language and, in general, of the modal logic, which go back to Leibniz.20 In both cases, both physics and language are treated within some general semantic approach. The circle is closed. Moreover, the modern Quantum logics are continuing Leibniz’s ideas of the last year of his life (1716), when he reconsidered, in the IV and V letters to Clarke, his own (now called Leibniz’s) principle of the identity of indiscernibles.[10] The violation of this principle in the world of Quantum phenomena is the main reason of the irreducible intensionality in the corresponding Quantum logics.21 Leibniz, as it seems, did not explain the reasons of his own predilection toward the intensional semantics; on the contrary, he always explained his intensional calculi in the extensional terms as well (calling such an extensional approach the “Scholastic” one [11, p.